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Question Number 197147 Answers: 2 Comments: 0

Question Number 197146 Answers: 1 Comments: 0

Find: Ω = ∫_0 ^( 1) ((Li(x))/(Ψ(x))) dx = ?

$$\mathrm{Find}:\:\:\:\Omega\:=\:\int_{\mathrm{0}} ^{\:\mathrm{1}} \:\frac{\mathrm{Li}\left(\mathrm{x}\right)}{\Psi\left(\mathrm{x}\right)}\:\mathrm{dx}\:=\:? \\ $$

Question Number 197133 Answers: 1 Comments: 0

Question Number 197132 Answers: 1 Comments: 1

∫^( +∞) _( 0) (((ln(t+(√(1+t^2 ))))/t))^2 =(π^2 /2)

$$\underset{\:\mathrm{0}} {\int}^{\:+\infty} \left(\frac{\mathrm{ln}\left(\mathrm{t}+\sqrt{\mathrm{1}+\mathrm{t}^{\mathrm{2}} }\right)}{\mathrm{t}}\right)^{\mathrm{2}} =\frac{\pi^{\mathrm{2}} }{\mathrm{2}} \\ $$

Question Number 197129 Answers: 2 Comments: 0

Question Number 197128 Answers: 1 Comments: 1

Question Number 197125 Answers: 1 Comments: 1

Question Number 197113 Answers: 1 Comments: 0

Prove that ∫^( +∞) _( 0) (((ln(t+(√(1+t^2 ))))/t))dt=(π^2 /2)

$$\mathrm{Prove}\:\mathrm{that} \\ $$$$\underset{\:\mathrm{0}} {\int}^{\:+\infty} \left(\frac{{ln}\left({t}+\sqrt{\mathrm{1}+{t}^{\mathrm{2}} }\right)}{{t}}\right){dt}=\frac{\pi^{\mathrm{2}} }{\mathrm{2}} \\ $$

Question Number 197112 Answers: 2 Comments: 0

Question Number 197111 Answers: 1 Comments: 0

∫_(π/4) ^(π/2) (dx/( (√(cos^3 x sin^5 x))))

$$\:\:\:\:\: \\ $$$$\:\:\:\:\underset{\pi/\mathrm{4}} {\overset{\pi/\mathrm{2}} {\int}}\:\frac{\mathrm{dx}}{\:\sqrt{\mathrm{cos}\:^{\mathrm{3}} \mathrm{x}\:\mathrm{sin}\:^{\mathrm{5}} \mathrm{x}}}\: \\ $$

Question Number 197110 Answers: 1 Comments: 0

Question Number 197104 Answers: 0 Comments: 3

Question Number 197099 Answers: 2 Comments: 0

∫^( (π/2)) _( 0) ((ln(cost))/(sint)) dt=???

$$\underset{\:\mathrm{0}} {\int}^{\:\frac{\pi}{\mathrm{2}}} \frac{\mathrm{ln}\left(\mathrm{cos}{t}\right)}{\mathrm{sin}{t}}\:\mathrm{d}{t}=??? \\ $$

Question Number 197095 Answers: 1 Comments: 0

Question Number 197094 Answers: 1 Comments: 0

Question Number 197089 Answers: 2 Comments: 0

Simplify (((1+(√3)i)/(1−(√3)i)))^(10)

$$\mathrm{Simplify}\:\left(\frac{\mathrm{1}+\sqrt{\mathrm{3}}\mathrm{i}}{\mathrm{1}−\sqrt{\mathrm{3}}\mathrm{i}}\right)^{\mathrm{10}} \\ $$

Question Number 197081 Answers: 0 Comments: 5

Question Number 197073 Answers: 1 Comments: 0

Question Number 197072 Answers: 2 Comments: 0

tan123=k tan167=?

$$\mathrm{tan123}=\boldsymbol{\mathrm{k}} \\ $$$$\mathrm{tan167}=? \\ $$

Question Number 197064 Answers: 2 Comments: 0

Question Number 197063 Answers: 1 Comments: 0

Question Number 197060 Answers: 1 Comments: 1

Prove that ∫^( (π/2)) _( 0) ((ln(1+αsint))/(sint))dt= (π^2 /8)−(1/2)(arccosα)^2

$$\mathrm{Prove}\:\mathrm{that}\: \\ $$$$\underset{\:\mathrm{0}} {\int}^{\:\frac{\pi}{\mathrm{2}}} \frac{\mathrm{ln}\left(\mathrm{1}+\alpha\mathrm{sin}{t}\right)}{\mathrm{sin}{t}}{dt}=\:\frac{\pi^{\mathrm{2}} }{\mathrm{8}}−\frac{\mathrm{1}}{\mathrm{2}}\left(\mathrm{arccos}\alpha\right)^{\mathrm{2}} \\ $$

Question Number 197057 Answers: 3 Comments: 2

Question Number 197054 Answers: 1 Comments: 0

lim_(x→(π/4)) ((sin^9 x−(1/2) cos^7 x)/(4x−π)) =?

$$\:\:\:\:\:\:\underset{{x}\rightarrow\frac{\pi}{\mathrm{4}}} {\mathrm{lim}}\:\frac{\mathrm{sin}\:^{\mathrm{9}} \mathrm{x}−\frac{\mathrm{1}}{\mathrm{2}}\:\mathrm{cos}\:^{\mathrm{7}} \mathrm{x}}{\mathrm{4x}−\pi}\:=? \\ $$

Question Number 197052 Answers: 1 Comments: 0

Find all the values of sin^(−1) (√2)

$$\mathrm{Find}\:\mathrm{all}\:\mathrm{the}\:\mathrm{values}\:\mathrm{of}\:\mathrm{sin}^{−\mathrm{1}} \sqrt{\mathrm{2}} \\ $$

Question Number 197050 Answers: 2 Comments: 4

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